Analyticity of nonlinear semigroups

The Cauchy problemdu/dt =Au(t),u(0) =u ₀∈D(A) has analytic solutions whenA has first and second Gateaux derivatives along the solution curve in a certain weak sense. HereA is a maximal monotone operator in a complex Hilbert space.     

Efficient calculations of coulombic interactions in biomolecular simulations with periodic boundary conditions

To make improved treatments of electrostatic interactions in biomacromolecular simulations, two possibilities are considered. The first is the famous particle–particle and particle–mesh (PPPM) method developed by Hockney and Eastwood, and the second is a new one developed here in their spirit but by the use of the multipole expansion technique suggested by Ladd. It is then numerically found that the new PPPM method gives more accurate results for a two-particle system at small separation of particles. Preliminary numerical examination of the various computational methods for a single configuration of a model BPTI–water system containing about 24,000 particles indicates that both of the PPPM methods give far more accurate values with reasonable computational cost than do the conventional truncation methods. It is concluded the two PPPM methods are nearly comparable in overall performance for the many-particle systems, although the first method has the drawback that the accuracy in the total electrostatic energy is not high for configurations of charged particles randomly generated. © 1993 John Wiley & Sons, Inc.     

Cycles intersecting a prescribed vertex set

A graph is said to have property P(k,l)(k ? l) if for any X ∈ (^G_k) there exists a cycle such that |X ∩ V(C)| = l. Obviously an n-connected graph (n ? 2) satisfies P(n,n). In this paper, we study parameters k and l such that every n-connected graph satisfies P(k,l). We show that for r = 1 or 2 every n-connected graph satisfies P(n + r,n). For r = 3, there are infinitely many 3-connected graphs that do not satisfy P(6,3). However, if n ? max{3,(2r ?1)(r + 1)}, then every n-connected graph satisfies P(n + r,n).     

On a conjecture of S. Reich

Simeon Reich (1974) proved that the fixed point theorem for single-valued mappings proved by Boyd and Wong can be generalized to multivalued mappings which map points into compact sets. He then asked (1983) whether his theorem can be extended to multivalued mappings whose range consists of bounded closed sets. In this note, we provide an affirmative answer for a certain subclass of Boyd-Wong contractive mappings.

     

Excited state reactions of amphiphilic Zn(II) porphyrin incorporated into liposomes as models for biological electron transfer

The amphiphilic porphinato zinc(II) complex (ZnP) containing four substituted amphiphilic alkyl chains was embedded in the liposomes of l,2-dipalmitoyl-sn-glycero-3phosphocholine. The distance from the embedded ZnP to the outer phase was changed from 9 to 27 ? by changing the substituted alkyl chain length. The electron transfer from the excited Zn complex to methylviologen (MV²⁺) or benzoquinone (BQ) added in the outer aqueous phase was studied. At first, quenching reactions were analyzed based on dynamic and static reaction models of the excited state. For the MV²⁺ quencher, only the triplet excited state of the embedded ZnP reacted, and electron transfer occurred at a distance less than 12 ?. In BQ both the singlet and the triplet excited states reacted, and the reaction of the singlet state was a static one indicating that BQ is incorporated into the liposomes. The distribution of the BQ molecule in the quenching sphere of ZnP was presented based on calculations assuming a stepwise incorporation into the quenching sphere.     

Roundabout relaxation: collective excitation requires a detour to equilibrium

Relaxation to equilibrium after strong and collective excitation is studied by using a Hamiltonian dynamical system of a one-dimensional XY model. After an excitation of a domain of K elements, the excitation is concentrated to fewer elements, which are made farther away from equilibrium, and the excitation intensity increases logarithmically with K. Equilibrium is reached only after taking this roundabout route, with the time for relaxation diverging asymptotically as Kgamma with gamma approximately 4.2.     

Magic number 7+/-2 in networks of threshold dynamics

Information processing by random feed-forward networks consisting of units with a sigmoidal input-output response is studied by focusing on the dependence of its outputs on the number of parallel paths M. It is found that the system leads to a combination of on-off outputs when M less or similar to 7, while for M greater or similar to 7, chaotic dynamics arises, resulting in a continuous distribution of outputs. This universality of the critical number M approximately 7 is explained by a combinatorial explosion, i.e., the dominance of factorial over exponential increase. The relevance of the result to biological problems is briefly discussed.     

Supply and waste management of radioisotopes in Japan

Radioisotopes have been widely used in Japan. The total number of facilities working with radioisotopes or radiation instruments reached to 5,509 in 1993. The state of supply of radioisotopes and management of radioactive wastes generated from the use of radioisotopes is described.     

Observation of helicity-induced Alfvén eigenmodes in large-helical-device plasmas heated by neutral-beam injection

The helicity-induced Alfvén eigenmodes (HAEs) with the toroidal mode number n=2 and 3 are observed for the first time in the Large Helical Device plasmas heated by neutral beam injection. The observed mode frequency is about 8 times higher than that of the observed toroidicity-induced Alfvén eigenmodes, and is proportional to the Alfvén velocity. The modes are excited when the ratio of the beam velocity to the Alfvén velocity exceeds about unity. The frequency lies just above the lower bound of the HAE gap in the plasma edge region of rho>0.7 (rho: normalized minor radius).